Question 80433: amazin' rainsin baking co. makes both raisin cake and raisin pie. a batch of raisin cakes requires 5 lbs. of flour, 2 lbs. of sugar, and 1 lb. of raisins. A batch of raisin pies requires 2 lbs. of flour, 3 lbs. of sugar and 4 lbs of raisins. there are 165 lbs. of flour, 110 lbs. of sugar and 120 lbs. of raisins available each week. Standing orders require at least five batches of raisin cakes and eight batches of raisin pies per week. If profit on a batch of raisin cakes is $35 and profit on a batch of raisin pies is $40, how many batches of each should be made per week to maximize profit?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! a batch of raisin cakes requires 5 lbs. of flour, 2 lbs. of sugar, and 1 lb. of raisins.
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A batch of raisin pies requires 2 lbs. of flour, 3 lbs. of sugar and 4 lbs of raisins.
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Let x = no. of batches of cakes, y = no. of batches of pies
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there are 165 lbs. of flour, 110 lbs. of sugar and 120 lbs. of raisins available each week.
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Write an equation for each ingredient, put in the form for graphing:
Flour: 5x + 2y =< 165
2y = 165 - 5x
y = 82.5 - 2.5x;
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Sugar: 2x + 3y =< 110
3y = 110 - 2x
y = 36.67 - .67x
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Raisins: x + 4y =<120
y = 30 - .25x
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Standing orders require at least five batches of raisin cakes and eight batches of raisin pies per week.
y => 8
x => 5
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Graph all the above, you have to add the vertical line at x = 5
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The corners of the feasibility region, rounded down if a fraction are
x | y
------
5 | 8
5 | 28
15| 26
25| 19
28| 8
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If profit on a batch of raisin cakes is $35 and profit on a batch of raisin pies is $40, how many batches of each should be made per week to maximize profit?
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35x + 40y = $profit
Substitute x & y from the above table
35(5) + 40(8) = $495
35(5) + 40(28) = $1295
35(15) + 40(26) =$1565
35(25) + 40(19) =$1635
35(28) + 40(8) = $1300
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You can see which Combination of cakes & pies are the most profitable, however
check each step here, there is much chance for error, I have confidence in the
method, but my math is often not so good
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